We put one of the predictions of adverse-selection models to the test, using data from the Danish automobile insurance market: that there is a positive correlation between claims risk and insurance coverage. We can find a statistically significant insurance coverage--risk correlation when coverage is expressed relative to the insurance premium, but not when it is expressed in monetary terms.

While extensive literature exists on the valuation and risk management of financial guarantees embedded in insurance contracts, both the corresponding longevity guarantees and interactions between financial and longevity guarantees are often ignored. The present paper provides a framework for a joint analysis of financial and longevity guarantees, and applies this framework to different annuity conversion options in deferred unit-linked annuities. In particular, we analyze and compare different versions of so-called guaranteed annuity options and guaranteed minimum income benefits with respect to the value of the option and the resulting risk for the insurer. Furthermore, we examine whether and to what extent an insurance company is able to reduce the risk by typical risk management strategies. The analysis is based on a combined stochastic model for both financial market and future survival probabilities. We show that different annuity conversion options have significantly different option values, and that different risk management strategies lead to a significantly different risk for the insurance company.

Albrecher et al. (Albrecher, H., Mayer Ph., Schoutens, W. (2008) General lower bounds for arithmetic Asian option prices. Applied Mathematical Finance, 15, 123–149) have proposed model-independent lower bounds for arithmetic Asian options. In this paper we provide an alternative and more elementary derivation of their results. We use the bounds as control variates to develop a simple Monte Carlo method for pricing contracts with Asian-style features. The conditioning idea that is inherent in our approach also inspires us to propose a new semi-analytic pricing approach. We compare both approaches and conclude that these both have their merits and are useful in practice. In particular, we point out that our newly proposed Monte Carlo method allows to deal with Asian-style products that appear in insurance (e.g., unit-linked contracts) in a very efficient way, and outperforms other known Monte Carlo methods that are based on control variates.

We consider the class of concave distortion risk measures to study how choice is influenced by the decision-maker's attitude to risk and provide comparative statics results. We also assume ambiguity about the probability distribution of the risk and consider a framework à la Klibanoff, Marinacci and Mukerji (2005; A smooth model of decision making under ambiguity. Econometrica, 73, 1849–1892) to study the value of information that resolves ambiguity. We show that this value increases with greater ambiguity, with greater ambiguity aversion, and in some cases with greater risk aversion. Finally, we examine whether a more risk-averse and a more ambiguity-averse individual will invest in more effort to shift his initial risk distribution to a better target distribution.

In the recent subprime mortgage crisis, which has caused banks and insurance companies to go bankrupt or into acquisition, the lender and insurer have exhibited not only correlated defaults when exposed to common risk factors but also counterparty default risk, which is triggered by mortgage defaults. Given the correlated defaults and the counterparty default risk, we use the reduced-form approach to derive the closed-form formulas of mortgage insurance contracts with premium refunds, annual premiums and upfront premiums. Regardless of the nature of the premium structures, the numerical analysis with parameter calibration demonstrates that both the correlated defaults and the counterparty default risk significantly impact mortgage insurance premiums, particularly in long-term mortgage loans.

The importance of funded private or occupational old-age provision is expected to increase due to demographic changes and the resulting problems for government-run pay-as-you-go systems. Clients and advisors therefore need reliable methodologies to match offered products with clients' needs and risk appetite. In Graf et al. (2012), the authors have introduced a methodology based on stochastic modeling to properly assess the risk-return profiles — i.e. the probability distribution of future benefits — of various old-age provision products. In this paper, we additionally consider the impact of inflation on the risk-return profile of old-age provision products. In a model with stochastic interest rates, stochastic inflation and equity returns including stochastic equity volatility, we derive risk-return-profiles for various types of existing unit-linked products with and without embedded guarantees and especially focus on the difference between nominal and real returns. We find that typical “rule of thumb” approximations for considering inflation risk are inappropriate and further show that products that are considered particularly safe by practitioners because of nominal guarantees may bear significant inflation risk. Finally, we propose product designs suitable to reduce inflation risk and investigate their risk-return profile in real terms.

In this paper, we develop a theoretical basis for drawing up a “Swedish” type actuarial balance sheet for a defined benefit pay-as-you-go (DB PAYG) scheme with retirement and disability benefits. Our model enables us to obtain the system's expected average turnover duration, measure the scheme's solvency and explore the phenomenon identified as “pension reclassification”, a widespread practice that masks the system's real status unless further pension information becomes available. The model is clearly linked to actuarial practice in social security and gives partial support to the practical adaptation of Swedish methodology carried out by OSFI (2012) in applying the concept of the contribution asset to the Canadian Pension Plan (CPP) balance sheet, which includes disability and survivor benefits.

This paper presents the design of optimal Bonus-Malus Systems using finite mixture models, extending the work of Lemaire (1995; Lemaire, J. (1995) Bonus-Malus Systems in Automobile Insurance. Norwell, MA: Kluwer) and Frangos and Vrontos (2001; Frangos, N. and Vrontos, S. (2001) Design of optimal bonus-malus systems with a frequency and a severity component on an individual basis in automobile insurance. ASTIN Bulletin, 31(1), 1–22). Specifically, for the frequency component we employ finite Poisson, Delaporte and Negative Binomial mixtures, while for the severity component we employ finite Exponential, Gamma, Weibull and Generalized Beta Type II mixtures, updating the posterior probability. We also consider the case of a finite Negative Binomial mixture and a finite Pareto mixture updating the posterior mean. The generalized Bonus-Malus Systems we propose, integrate risk classification and experience rating by taking into account both the a priori and a posteriori characteristics of each policyholder.

Modelling automobile insurance claims is a crucial component in the ratemaking procedure. This paper focuses on the probability that a policyholder reports a claim, where the classical logit link does not provide a right model. This is so because databases related with automobile claims are often unbalanced, containing more non-claims than the presence of claims. In this work an asymmetric logit model, which takes into account the large number of non-claims in the portfolio, is considered. Both, logit and asymmetric logit models from a Bayesian point of view, are used to a sample that was collected from a major automobile insurance company in Spain in 2009, resulting in a dataset of 2,000 passenger vehicle. We establish the validity of the asymmetric model in front of the conventional logit link. The use of a garage, the age of the vehicle and the duration of the client's relation with the company are all shown to be significant explanatory variables by the logit model. The asymmetric model includes, in addition, the length of time the policyholder has held a driving licence and the type of use made of the vehicle. The asymmetric model provides a better fit to the data examined.

We consider the optimal dividend control problem to find an optimal strategy under the constraint that dividend rates is restricted such that the expected total discounted dividends are maximized for an insurance company. The evolution of the reserve is modeled by a diffusion process with drift and volatility coefficients modulated by an observable Markov chain. We consider the regime-switching threshold strategy which pays out dividends at the maximal possible rate when the current reserve is above some critical level dependent on the regime of the Markov chain at the time, and pays nothing when the reserve is below that level. We give sufficient conditions under which such type of strategy is optimal for the regime-switching model.